Molecular Simulation and Systems Biology - Systems Biology: Networks, Models, and Applications - page 81

formation of covalent bonds, and therefore need to be treated quantum
mechanically. Although it is not practical to model an entire protein
quantum mechanically, hybrid quantum mechanical/molecular
mechanical (QM/MM) methods have been developed. QM/MM
methods embed a small quantum mechanical region (e.g., the substrate
and active site side chains) in a larger context of molecular mechanics
atoms (the surrounding protein and solvent). These methods were
pioneered for the study of the reaction pathway of triosephosphate
isomerase [29]. There is an extensive literature discussing the specific
ways enzymes accelerate reactions [30-32], but the general mechanism
involves decreasing the activation free energy for the reaction—in
effect, stabilizing the transition state relative to the reactants.
Biomolecular simulations are not limited to proteins or other
biopolymers. Simulations have contributed a great deal of detail to
our understanding of other biological structures such as the lipid bilay-
ers that make up cell membranes. The first simulation of a simplified
bilayer was carried out in 1982 [33]. Because of computational resource
limitations, the membrane was modeled as a bilayer of united atom
aliphatic chains with an empirical restraint potential replacing the
water above and below the membrane. The resulting 320 atoms were
simulated for a total of 80 ps.
Computer power is starting to reach the point where biomolecular
simulations can access the time scales and degree of sampling neces-
sary to provide important insights into the thermodynamics and
kinetics of protein folding. The first folding free energy landscape of
a protein in explicit water was calculated by Boczko and Brooks in
1995 [34]. By examining the free energy of the protein as a function of
a specific coordinate, such as the radius of gyration, it is possible to
find potential transition states for folding and get a better picture of
the set of conformations that are sampled by the protein at a particular
temperature. In order to determine the free energy landscape, Boczko
and Brooks combined data from a large number of separate simula-
tions, each of which restrained the protein to a particular range of
values for selected order parameters like the radius of gyration and
fraction of native contacts. This allowed them to build up the free
energy landscape for folding without simulating the 10 9 -10 15 time

steps necessary to simulate a folding event.
The direct, long time scale simulation of protein folding is a formi-
dable technical challenge. The longest single atomistic trajectory of
a protein in water to date was carried out by Duan and Kollman in
1998 [21]. They simulated the 36-residue villin headpiece for 1 10 8

time steps) starting from a thermally unfolded state. During the simu-
lation, early events in protein folding such as helix formation and
hydrophobic collapse were observed. In addition, the simulation
clearly shows the protein collapsing and expanding as it searches for

µ s (5 ×